The cooling apparatus of the engine according to the invention supplies the cooling water directly to the cylinder block water passage from the cylinder head water passage when the engine temperature is between first and second temperatures, and a supply of the cooling water to the heat exchanger is not requested. The first and second temperatures are lower than the engine completely-warmed temperature. The apparatus supplies the cooling water discharged from the cylinder block and head water passages, to the water passages through the heat exchanger when the engine temperature is between the second temperature and the engine completely-warmed temperature, and the supply of the cooling water to the heat exchanger is not requested.